Geometry is an a priori science. However, its apriority is saddled with problems. The aim of this paper will be to show 1) how Kant understands that the contents of geometry are synthetic a priori judgments in the Critique of Pure Reason, and 2) if it’s still relevant to study Kant’s theory of geometry after the challenges posed by non-Euclidian theories of space. With respect to point 1: Kant understands geometry as the discipline that objectifies the pure intuition of space. Every geometric concept is built upon the pure intuition of space through a synthetic ostensive process. Furthermore, the pure intuition of space is the form of external experiences. Thus, geometry and external phenomena share a common ground – pure space. This common ground is what provides an answer to the question of the possibility of mathematics as a universal and a priori science. With respect to point 2: the relevance of studying Kant’s theory of geometry lies not only in the fact that geometry can serve as an example to philosophy based on the fact that it establishes its propositions a priori, but also because the object-study of geometry – the pure intuition of space– forces the reader to review Kant’s thoughts about sensibility and its relation to space. The analysis of Kant’s theory of geometry then amounts to studying Kant’s theory of sensibility. / Para Kant la geometría es una disciplina matemática que contiene proposiciones y juicios sintéticos a priori. Sin embargo, esta afirmación no se encuentra libre de problemas. La intención del artículo será mostrar 1) cómo entiende Kant la apodicticidad, universalidad y sinteticidad de la geometría en la Crítica de la razón pura; y 2) qué relevancia tiene hoy en día estudiar la teoría kantiana de la geometría luego de la superación de la teoría euclidiana del espacio. Con respecto a (1): Kant entiende a la geometría como la ciencia que objetiva la intuición pura del espacio. Todo concepto geométrico se construye en la intuición del espacio mediante un proceso sintético que exhibe la figura geométrica. Además, la intuición pura del espacio es la forma del sentido externo. Por tanto, los objetos geométricos y los fenómenos externos comparten un territorio común: el espacio como intuición pura. Este aspecto común garantiza la universidad de la geometría. Con respecto a (2): la importancia de estudiar la teoría kantiana de la geometría no solo radica en que esta disciplina determina a priori su objeto y por tanto sirve de ejemplo a la filosofía, sino que la comprensión del objeto de la geometría, el espacio como intuición pura, nos obliga a pasar revista a lo qué entiende Kant por sensibilidad y su relación con el espacio. El estudio de la sensibilidad obliga a Kant a repensar qué se entiende por espacio y, con ello, qué se entiende por geometría. El análisis de la teoría kantiana de la geometría, entonces, equivale al estudio de la teoría kantiana de la sensibilidad.

Em mecânica dos fluidos, especificamente em processos turbulentos, o problema de fechamento representa um dos maiores desafios para qualquer pessoa interessada nesta área. Durante décadas, cientistas vêm usando abordagens estatísticas com o objetivo de \"fechar\" o problema ou, pelo menos, diminuir as dificuldades inerentes. Assim, o presente trabalho apresenta uma criteriosa análise com base em ferramentas estatísticas em que ondas quadradas aleatórias, aliadas a um número fixo de parâmetros, foram utilizadas para criar equações paramétricas para representar um fluxo turbulento unidimensional com uma abordagem a priori, diferenciando de outras abordagens aplicadas amplamente na área, que utilizam uma abordagem a posteriori. Em seguida, simulações foram realizadas, a fim de avaliar o comportamento do modelo. Nas simulações pôde-se reproduzir o comportamento observado na literatura e estipular a abrangência do método. Além disso, uma importante discussão acerca das condições de contorno foi desenvolvida. / In fluid mechanics, specifically in turbulent processes, the closure problem represents one of the biggest challenges for anyone interested in this area. For decades, scientists have been using statistical approaches aiming to close the problem or, at least, decrease the inherent difficulties. So, the present project presents a judicious analyze based on statistical tools in which random square waves, allied with a fixed numbers of parameters, were used to create parametric equations to represent a turbulent flow with an a priori approach, differentiating from other approaches broadly applied in the area, which use an a posteriori approach. Then simulations were done, in order to evaluate the behavior of the model. In the simulations, the behavior of some data from the literature could be followed and the scope of the method was stipulated. Besides this, an important discussion about boundary conditions was developed.

In this thesis, we interrogate the possibility of freedom presupposed by the project of philosophical critique developed by late Foucault, which aims both at analysis of historical a priori conditions and at disruption of our present a priori. The first chapter shows that this critical project can be traced back to Foucault's early works. Moreover, Foucault tackled the problem of freedom in every phase of his work and he kept proposing the same solution, namely, that the spaces of freedom are opened up by ruptures emerging within the system governing a given period. Next, different concepts of freedom present in Foucault's texts are distinguished. On this basis, it is possible to restate the question of critic's freedom, which we now define as the problem of articulation between the ontological freedom, the reflective freedom and the freedom of transformation. The second chapter is devoted to Foucault's archaeological period. First, we show how the conception presented in The Order of the Things leads to aporias regarding the question of freedom. Next, we describe the theoretical transformations carried out in The Archaeology of Knowledge and examine whether Foucault succeeded in eliminating the earlier difficulties. However, this later solution also turns out to be unsatisfactory, because it falls...

International Telemetering Conference Proceedings / October 23-26, 2000 / Town & Country Hotel and Conference Center, San Diego, California / A thinned array sensor system develops error voltages for steering dish antennas from signals arriving over a broad range of angles, thereby eliminating need for a priori knowledge of signal location.

La segmentation d'image avec a priori de forme a fait l'objet d'une attention particulière ces dernières années. La plupart des travaux existants reposent sur des espaces de formes linéarisés avec de petits modes de déformations autour d'une forme moyenne. Cette approche n'est pertinente que lorsque les formes sont relativement similaires. Dans cette thèse, nous introduisons un nouveau cadre dans lequel il est possible de manipuler des a priori de formes plus généraux. Nous modélisons une catégorie de formes comme une variété de dimension finie, la variété des formes a priori, que nous analysons à l'aide d'échantillons de formes en utilisant des techniques de réduction de dimension telles que les diffusion maps. Un plongement dans un espace réduit est alors appris à partir des échantillons. Cependant, ce modèle ne fournit pas d'opérateur de projection explicite sur la variété sous-jacente et nous nous attaquons à ce problème. Les contributions de ce travail se divisent en trois parties. Tout d'abord, nous proposons différentes solutions au problème des "out-of-sample" et nous définissons trois forces attirantes dirigées vers la variété. 1. Projection vers le point le plus proche; 2. Projection ayant la même valeur de plongement; 3. Projection à valeur de plongement constant. Ensuite, nous introduisons un terme d'a-priori de formes pour les coutours/régions actifs/ves. Un terme d'énergie non-linéaire est alors construit pour attirer les formes vers la variété. Enfin, nous décrivons un cadre variationnel pour le debruitage de variété. Des résultats sur des objets réels tels que des silhouettes de voitures ou des structures anatomiques montrent les possibilités de notre méthode.

Thesis advisor: Olivier Boulnois / Thesis advisor: Stephen F. Brown / The Dissertation Text has Three Parts. Each paragraph is referred at the end to the Part it summarizes. My dissertation places Saint Anselm’s Ontological Argument within its original Neoplatonic context that should justify its validity. The historical thesis is that Anselm’s epistemology, underlying the Proslogion, the Monologion and De Veritate, was a natural, often unaccounted for, reflection of the essentially Neoplatonic vision that defined the pre-thirteenth century mental culture in Europe. (Introduction and Part I) This thesis is shown through the reception of Anselm’s argument by 27 XIIIth-XIVth century thinkers, whose reading of it exhibits a gradual weakening of Neoplatonic premises up to a complete change of paradigm towards the XIVth century, the first reason being the specificity of the Medieval reception of Aristotle’s teaching on first principles that is the subject of Posterior Analytics (Part II), and the second reason being the specificity of the Medieval reception of Dionysius the Areopagite (Part III, see sub-thesis 4 below). The defense of this main historical thesis aims at proving three systematic sub-theses, including a further historical sub-thesis. The Three Systematic Sub-Theses: 1) The inadequacy of rationalist and idealist epistemology in reaching and providing apodictic truths (the chief one of which is God’s existence) with ultimate ontic grounding, as well as the inadequacy of objectivistic metaphysics that underlies these epistemologies, calls for another, non-objectifying epistemic paradigm offered by the Neoplatonic (Proclian theorem of transcendence) apophatic and supra-discursive logic (kenotic epistemology) that should be a better method to achieve certainty, because of its ability to found logic in its ontic source and thus envisage thought as an experience and a mode of being in which it is grounded. Within such a dialectic, there cannot be any opposition or division either between being and thought, or between faith and reason, faith being an ontic ground of reason’s activity defined as self-transcendence. The argument of the Proslogion is thus an instance of logic that transcends itself into its own principle – into ‘that than which nothing greater can be conceived’. Such an epistemological vision is also supported by contemporary epistemology (Russell’s Paradox and Gödel’s Incompleteness Theorem) (Introduction and Part I) 2) In virtue of this apophatic and supra-discursive vision, God’s existence, thought by human mind (as expressed in the argument of the Proslogion), happens to be a common denominator between God’s inaccessible essence and the created essence of human mind, so that human consciousness can be defined as ‘con-science’ – the mind experiencing its own being as co-knowledge with God that forges being as such. (Part I) 3) However, God’s existence as a common denominator between God’s essence and the created essence of human mind cannot be legitimately accommodated within the XIIIth-XIVth century epistemology and metaphysics because of the specificity of relation between God’s essence and His attributes, typical of Medieval scholasticism and as stated by Peter Lombard and Thomas Aquinas. If this relation is kept, while at the same time God’s existence is affirmed as immanent to the human mind (God as the first object of intellect), God’s transcendence is sacrificed and He becomes subject to metaphysics (Scotus’ nominal univocity of being). In order to achieve real univocity between the existence of human thinking and God’s existence, one needs a relation between God’s essence and His attributes that would allow a real participation of the created in the uncreated. The configuration of such a relation, however, needs the distinction between God’s essence and His energies that Western Medieval thought did not know, but that is inherent to the Neoplatonic epistemic tradition persisting through the Eastern Church theologians and Dionysius the Areopagite up to Gregory Palamas. (Part III) Another Historical Sub-Thesis: 4) One of the reasons why Medieval readers of Anselm’s Proslogion misread it in the Aristotelian key, was that they did not have access to the original work of Dionysius the Areopagite, in which the said distinction between God’s essence and His energies is present. This is due to the fact that the Medievals read Dionysius through Eriugena’s translation. However, Eriugena was himself influenced by Augustine’s De Trinitate that exhibits an essentialist theology: in fact, it places ideas within God’s essence, which yields the notion of the created as a mere similitude, not real participation, and which ultimately makes the vision (knowledge) of God possible only in the afterlife. Since already with Augustine the relation between grace and nature is modified (grace becomes a created manifestation of God, instead of being His uncreated energy), God’s essence remains incommunicable. Similarly, God’s existence is not in any way immanent to the created world, of which the created human intellect is a part, so that it remains as transcendent to the human mind as is His incommunicable essence. This should explain why for the Medievals analogy, and eventually univocity, was the only way to say something about God, and also why they mostly could not read Anselm’s Proslogion otherwise than either in terms of propositional or modal logic. (Part III) The dissertation concludes that whilst Anselm’s epistemology in the Proslogion is an instance of Neoplatonic metaphysical tradition, the question of the possibility of certainty in epistemology, as well as the possibility of metaphysics as such, depends on the possibility of real communicability between the immanence of human predicating mind and the transcendence of God’s essence through His trans-immanent existence.

The purpose of confidence and prediction intervals is to provide an interval estimation for an unknown distribution parameter or the future value of a phenomenon. In many applications, prior knowledge about the distribution parameter is available, but rarely made use of, unless in a Bayesian framework. This thesis provides exact frequentist confidence intervals of minimal volume exploiting prior information. The scheme is applied to distribution parameters of the binomial and the Poisson distribution. The Bayesian approach to obtain intervals on a distribution parameter in form of credibility intervals is considered, with particular emphasis on the binomial distribution. An application of interval estimation is found in auditing, where two-sided intervals of Stringer type are meant to contain the mean of a zero-inflated population. In the context of time series analysis, covariates are supposed to improve the prediction of future values. Exponential smoothing with covariates as an extension of the popular forecasting method exponential smoothing is considered in this thesis. A double-seasonality version of it is applied to forecast hourly electricity load under the use of meteorological covariates. Different kinds of prediction intervals for exponential smoothing with covariates are formulated. / Konfidenz- und Prognoseintervalle dienen der Intervallschätzung unbekannter Verteilungsparameter und künftiger Werte eines Phänomens. In vielen Anwendungen steht Vorinformation über einen Verteilungsparameter zur Verfügung, doch nur selten wird außerhalb von bayesscher Statistik davon Gebrauch gemacht. In dieser Dissertation werden exakte frequentistische Konfidenzintervalle unter Vorinformation kleinsten Volumens dargelegt. Das Schema wird auf Verteilungsparameter für die Binomial- und die Poissonverteilung angewandt. Der bayessche Ansatz von Intervallen für Verteilungsparameter wird in Form von Vertrauensintervallen behandelt, mit Fokus auf die Binomialverteilung. Anwendung findet Intervallschätzung in der Wirtschaftsprüfung, wo zweiseitige Intervalle vom Stringer-Typ den Mittelwert in Grundgesamtheiten mit vielen Nullern enthalten sollen. Im Zusammenhang mit Zeitreihenanalyse dienen Kovariaten der Verbesserung von Vorhersagen zukünftiger Werte. Diese Arbeit beschäftigt sich mit exponentieller Glättung mit Kovariaten als eine Erweiterung der gängigen Prognosemethode der exponentiellen Glättung. Eine Version des Modells, welche doppelte Saison berücksichtigt, wird in der Prognose des stündlichen Elektrizitätsbedarfs unter Zuhilfenahme von meteorologischen Variablen eingesetzt. Verschiedene Arten von Prognoseintervallen für exponentielle Glättung mit Kovariaten werden beschrieben.

Kant's critical philosophy promises to overturn both Empiricism and Rationalism by arguing for the necessity of a passive faculty, sensibility, and an active faculty, understanding, in order for cognition to obtain. Kant argues in favor of sense impression found in standard empirical philosophies while advocating conceptual necessities like those found in rational philosophies. It is only in the synthesis of these two elements that cognition and knowledge claims are possible. However, by affirming such a dualism, Kant has created yet another problem familiar to the history of philosophy, one of faculty interaction. By affirming two separate and exclusive capacities necessary for cognition, Kant has bridged the gap between the two philosophical traditions, but created a gap that must be overcome in order to affirm his positive programmatic. Kant himself realizes the difficulty his new philosophy faces when he claims the two sources of knowledge must have a "common, but unknown root." To complete Kant's program one must ask: "What bridges the gap between sensible intuition and conceptual understanding?" In my dissertation, I turn to Kant's philosophy and find the answer to this question in the productive imagination. In order to evaluate the viability of this answer, I problematize the imagination as it has been found in the history of Western philosophy. By tracing the historical use of the imagination in archetypal figures from both empiricist and rationalist traditions, one finds a development of imagination that culminates in the fundamental formulation found in Kant's Critique of Pure Reason. In his critical philosophy, Kant synthesizes the imagination (Einbildungskraft) and the use of imagination found in both traditions, thus demonstrating its role in both sensation and understanding. By employing the imagination at both sensorial and conceptual levels, Kant has found, I argue, the liaison that overcomes the dualism established by his requirements for knowledge, as well as the common root for both.

Hannover, Univ., Diss., 2004.

Techn. Hochsch., Diss., 2000--Aachen.